Question

given the points - 4 ,8 and 6 ,- 12 a determine the midpoint of the line segment connecting points
b determine the distance separating the two points​

Answer 1

Step-by-step explanation:

Given:

The points are (-4, 8) and (6, -12)

Using Mid-point formula ,

$x = \frac{x1 + x2}{2} = \frac{ - 4 + 6}{2} = \frac{2}{2} = 1$

$y = \frac{y1 + y2}{2} = \frac{8 - 12}{2} = \frac{ - 4}{2} = - 2$

So, the mid-point of the line segments is (1, -2)

Now,

Distance between the two points is :

Using distance formula,

$d = \sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }$

$d = \sqrt{(6 - ( - 4))^{2} + ( - 12 - 8)^{2} }$

$d = \sqrt{( 10)^{2} + ( - 20)^{2} }$

$d = \sqrt{100 + 400 }$

$d = \sqrt{500 } = 10 \sqrt{5} \: units$

Hope you understand it

Thank you